The Cape High Court agreed to a deal for Thatcher to pay a fine of 3 million rand ($500,000) or face five years in jail in South Africa, in addition to a further four-year prison sentence suspended for five years.
Prosecutors said Thatcher was free to leave South Africa.
"There is no price too high for me to pay to be reunited with my family and I am sure all of you who are husbands and fathers would agree with that," Thatcher said on Thursday on the steps of the court after the hearing.
Save me mummy
A mocking banner strung from the third storey of an office block opposite the courthouse read "Save me mummy". It was not clear who placed it. On the steps outside the court one man chanted "shame on you, shame on you".
Thatcher also agreed to assist South African investigations into the plot against the government of Equatorial Guinea, a tiny country flush with newly-found oil wealth.
Margaret Thatcher visited her
son in South Africa at Christmas
Immaculately dressed in a dark suit and gold coloured tie, a nervous-looking Thatcher repeatedly said "yes I do" when asked in court whether he agreed to the various terms of the deal, which allows him to leave South Africa to join his family in America for the first time in nearly five months.
His American-born wife Diane took their two children to the US shortly after his arrest, but returned to Cape Town to be with him. Margaret Thatcher visited her son at Christmas.
Thatcher, 51, pleaded guilty to attempting to contravene section 2 of South Africa's anti-mercenary Regulation of Foreign Military Assistance Act by agreeing to charter a helicopter, for which he paid a total of $275,000.
"The accused began to suspect that the helicopter might in fact be intended for use in ... mercenary activity [in the west African region]. Despite his misgivings the accused decided to invest money in the charter of the helicopter," said the text of the agreement, which was handed to journalists.
"It should be noted that Sir Mark was not charged with any involvement in the attempted coup d'etat in Equatorial Guinea. The plea bargain was entered into solely as a result of his financing of the charter of a helicopter in circumstances where he should have exercised more caution," Thatcher's lawyers said in a separate statement.
"There is no price too high for me to pay to be reunited with my family and I am sure all of you who are husbands and fathers would agree with that"
Asked if he had got off lightly, the spokesman for South Africa's elite Scorpions investigation unit, Sipho Ngwema, said: "Mr Mark Thatcher has agreed to cooperate fully with the investigations, so we are happy."
Thatcher, who has lived for the past eight years in South Africa where he has permanent residency, was arrested in Cape Town last 25 August on charges of bankrolling a foiled coup in Equatorial Guinea.
That country sentenced 11 foreigners in November to between 14 and 34 years in jail for their role in the plot, and two of its own citizens to 16 months in a trial denounced as "grossly unfair" by UK-based human rights group Amnesty International.
Zimbabwe jailed Thatcher's long-term friend and former British special services officer Simon Mann in September along with 65 other suspected mercenaries.